Synchronization Of Stochastic Coupled Delay Reaction-diffusion Systems

Complex network is a coupled system composed of a large number of interconnected dynamic nodes,which has been widely applied in many fields,such as Internet,global economic markets,social networks and ecosystems.The research of complex network synchronization phenomenon is of great theoretical and practical value.Since the system state moves with space and time in most of the actual systems,the diffusion effects are unavoidable.Moreover,time delay and stochastic perturbation are common phenomenon.The stochastic coupled delay reaction-diffusion systems(SCDRDSs)taking the above factors into consideration can describe the change laws of things in nature more accurately.Based on this point,this paper considers the synchronization problem of SCDRDSs.At the beginning,the research background and significance of the SCDRDSs and the research status at home and abroad are introduced.Moreover,stochastically asymptotical synchronization and mean square H-infinity synchronization of SCDRDSs via boundary control are studied.By constructing suitable Lyapunov functional and using the Schur complement lemma,boundary controllers for Neumann boundary conditions and mixed boundary conditions are designed respectively,and sufficient criteria for stochastically asymptotical synchronization based on linear matrix inequality are obtained.When a system is affected by external additive noise,mean square H-infinity synchronization for SCDRDSs with Neumann boundary conditions and mixed boundary conditions is studied.The sufficient criteria for H-infinity synchronization are proposed via designing different boundary controllers.Last but not least,finite-time synchronization and H-infinity synchronization of stochastic coupled delay impulsive reaction-diffusion systems in the mean square are studied.By constructing appropriate Lyapunov-Krasovskii functional and Gronwall's inequality,sufficient criterion for mean square finite-time synchronization is established under the representation of bounded impulsive interval,and this criterion is related to the impulsive frequency,impulsive strength,system coefficients and time-delay.When the system is affected by external interference,the sufficient criterion for mean square H-infinity synchronization is provided,and the effect of spatial regions on the H-infinity synchronization is put forward.In addition,the theoretical results in this paper are supported by numerical examples.